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Evolution was the development and change of organisms over time. It is closely linked to mutation and natural selection, although specifically it is a long-term process of adaptation, concerning the development of species in relation to "survival of the fittest."
Evolution took place over aeons. The Eighth Doctor once stated that evolution didn't work backwards. (AUDIO: Scherzo) However, it was believed the Macra had "devolved," having once been empire-builders, but eventually becoming savage beasts in the far future. (TV: Gridlock)
Evolution usually began with creatures emerging from a "primordial soup." While the process took time, accelerated evolution could be achieved such as when Josiah Samuel Smith and Control evolved through different forms during their centuries on Earth, eventually evolving into a "Victorian gentleman" and "lady." (TV: Ghost Light)
Davros wished to determine the ultimate evolution of the Kaled race and to direct it. The result of this was the Daleks. (TV: Genesis of the Daleks) After escaping the Battle of Canary Wharf, Dalek Sec and the Cult of Skaro arrived in 1930s New York. Dalek Sec wished to determine the ultimate evolution of the Daleks, which resulted in the human-Dalek. (TV: Daleks in Manhattan / Evolution of the Daleks)
Light and the Reverend Ernest Matthews separately found the concept abhorrent, though for different reasons, the former because of his love of stasis and hatred of change, the latter because he found it repugnant to have evolved from monkeys. (TV: Ghost Light)
Professor Richard Lazarus had created a machine that rejuvenated himself, or, in simpler terms, a machine that allowed him to make himself younger. This transformation also accidentally unlocked a rejected option for human evolution, making him a scorpion-like mutant. (TV: The Lazarus Experiment)
The Time Lords evolved over time into what they were at the time of the Time War, through prolongued exposure to the Time Vortex. River Song was experimented on to have similar characteristics after having been conceived in the Vortex. (TV: A Good Man Goes to War)
The Seventh Doctor told Ace that examples of actual evolution are quite rare in Earth science, and that the universe was big enough for all the conflicting theories of species development to have some validity. (PROSE: Cat's Cradle: Witch Mark)